Terms and Definitions

Symbols, Descriptions and Units

SymbolMeaningMetric Units
CijElastic stiffness constantnewton/meter2
C0Shunt capacitancefarad
C1Series capacitancefarad
dijPiezoelectric strain constantscoulomb/newton
d33Piezoelectric strain constant x 10-12 Meter/Volt
d31Piezoelectric strain constantx 10-12 Meter/Volt
d15Piezoelectric strain constantx 10-12 Meter/Volt
EElectric fieldV/m
faAntiresonance frequencycycles/second
frResonance frequencycycles/second
fnFrequency of max. impedancecycles/second
fmFrequency of min. impedancecycles/second
fpParallel resonance frequencycycles/second
fsSeries resonance frequencycycles/second
gijPiezoelectric voltage constantsmeter2/coulomb
g33Piezoelectric voltage constantX 10-3 voltmeter/newton
g31Piezoelectric voltage constantX 10-3 voltmeter/newton
g15Piezoelectric voltage constantX 10-3 voltmeter/newton
hijPiezoelectric pressure constantsnewton/coulomb
KijElectromechanical coupling constant
k31Transverse coupling constant
k33Longitudinal coupling constant
k15Shear coupling constant
ktThickness coupling constant
kpPlanar coupling constant
KTFree relative dielectric constant
KSClamped relative dielectric constant
PElectric polarizationcoulomb/meter2
QMMechanical quality factor
QEElectrical quality factor
SijElastic compliance constantmeter2/newton

Terms and Definitions

Curie Point

The temperature at which the dielectric constant peaks and all polarization disappears.

Coupling Coefficient (k)

A dimensionless number related to the ratio of the energy stored in the mechanical and electrical portions of the material. The first subscript indicates the direction of the electric field and the second indicates the direction of the mechanical strain, expressed in percent.


The ratio of mass to volume in the material, expressed in kg/m3.

Dielectric Constant

The ratio of the permitivity of the material to the permitivity of free space. The value specified is for the "free" condition (i.e., unclamped and well below the mechanical resonance of the part).

Dissipation Factor

A measure of the dielectric losses in the material defined as the tangent of the loss angle or the ratio of parallel resistance to parallel reactance expressed in percent.

"d" Constant

The piezoelectric constant relating mechanical strain and applied electric field - defined as the ratio of strain to field. The first subscript indicates the direction of the field and the second the direction of the resulting strain, expressed in meters/volt.


The ratio of voltage developed to the distance between the electrodes.

Frequency Constant

Defined as the resonant frequency (fr) times the controlling dimension, expressed in KHz-m.

"g" Constant

The piezoelectric constant relating open circuit voltage and mechanical stress - defined as the ratio of voltage to stress. The first subscript indicates the direction of the generated voltage, and the second indicates the direction of the force, expressed in volt-meters/newton.

Mechanical Q (QM)

The ratio of reactance to resistance in the equivalent electric series circuit representing the mechanical vibrating resonant system. The shape of the part affects the value.


The ratio of the change in length to the length.


The ratio of applied force to the cross sectional area.

Young's Modulus (Y)

The mechanial stiffness property of a piezoelectric ceramic material and is expressed as the ratio or stress to strain the material, while vibrating at its resonant frequency, expressed in newtons/meter2.